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by Fred Schenkelberg 2 Comments

Sample Size Problem

Sample Size Problem

Let’s work a sample size problem.

A random sample size, n, is to be taken from a large population having a standard deviation of 1″. The sample size is to be determined so that there well be a 0.05 risk probability of exceeding a 0.1″ tolerance error in using the sample mean to estimate μ. Which of the following values is nearest the required sample size?

a. 42

b. 106

c. 203

d. 384

Please work out your answer, add a comment with your result and show your work, please. Don’t peek at the comments if you’ve not worked it yet.

[note to self: find a way to use a multiple choice feature that tallies the results]

This problem from the Quality Council of Indiana with permission.


Related:

Sample Size – success testing (article)

Sample size (article)

Hypothesis Test Sample Size (article)

 

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: sample size, Sample Size Determination, Standard Deviation

« Sample size
Question a Day Idea »

Comments

  1. Bandar Abualnassr says

    October 28, 2012 at 2:41 AM

    n = ( z^2 * σ^2 ) / ME^2

    To find z:
    the cumulative probability is 1 – alpha/2 = 1 – 0.05/2 = 0.975
    from z table, for 0.97 z=1.96

    ME = 0.1″
    σ = 1

    so, n = ( 1.96^2 * 1^2 ) / 0.1^2 = 384.16
    So, correct answer is D.

    Thanks for the question Fred.

    Reply
    • Fred Schenkelberg says

      October 28, 2012 at 10:48 AM

      Correct – I found that having the most common values of the z-table ready to go, did save time. Alpha of .01, .05, .1 for example. And, knowing how to use the table for that question that was for alpha of .03 for some reason.

      Reply

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